AQA Further AS Paper 2 Discrete 2023 June — Question 7 2 marks

Exam BoardAQA
ModuleFurther AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year2023
SessionJune
Marks2
TopicMinimum Spanning Trees

7 A construction company has built eight wind turbines on a moorland site. The network below shows nodes which represent the site entrance, \(E\), and the wind turbine positions, \(S , T , \ldots , Z\)
\includegraphics[max width=\textwidth, alt={}, center]{372edcfa-c3cd-4c83-89e9-2bb5fd9825f1-12_924_1294_479_356} Each arc represents an access track with its length given in metres.
These 17 tracks were created in order to build the wind turbines. Eight of the tracks are to be retained so that each turbine can be accessed for maintenance, directly or indirectly, from the site entrance. The other nine tracks will be removed. 7
    1. To save money the construction company wants to maximise the total length of the eight tracks to be retained. Determine which tracks the construction company should retain.
      7
  1. (ii) Find the total length of the eight tracks that are to be retained. 7
  2. The total length of the 17 tracks is 14.6 km
    The cost of removing all 17 tracks would be \(\pounds 87,600\)
    Using your answer to part (a)(ii), calculate an estimate for the cost of removing the nine tracks that will not be retained.
    [0pt] [2 marks]
    7
  3. Comment on why the modelling used in part (b) may not give an accurate estimate for the cost of removing the nine tracks.